Hey Sunworshiper, I read several articles on pruning lychees and you just have to be sure that you are not confusing varieties. I know there was at least on article that discussed pruning of Kaimana at a certain time to significantly increase yields but the same article said there was no significant difference in yield when several other varieties were pruned.
I would drop lycheesonline an email or give them a call. In my opinion, I would not prune right now as you have stated that the leaves are grown out already and are currently hardening. If you prune now, you would loose a lot of growth on an already small and dwarf type tree. If you prune now, it will likely induce another flush, veg or floral, only Mother Nature knows but you do know that your tree recently spent a good amount of energy on its current flush. You would be draining the stored energy by inducing another flush now which will likely reduce yield or drop the stored reserves in your tree below the critical mass required for fruiting so you may just get another veg flush.
Exactly how large is your tree? If it's large enough and you really must have fruit this year, you can take a chance pruning now, if your tree is large enough, it may have resources to bloom and fruit. You may also consider girdling a branch without pruning if your tree is large enough. Do not give any Mitrogen fertilizer right now. I would give your tree some organic 0-10-10 right now and also foliar feed with kelp emulsion today.
If I were you, I would let your tree do its own thing and get larger. You may still be able to get this veg flush to harden off, rest, and if you get a late cold snap, you could get fruit. emperors fruit pretty consistently when they are established from what I have seen. Patience as a virtue is often tought but all too often rarely practiced.